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NCERT Solutions for Class 9th Science Chapter 4 In-text Questions — Uniform circular motion

Book page 66 Updated on2026-09-08

Q1.
What is the distance travelled by the child? What is their displacement from their original position?
Answer

The child on the merry-go-round moves from A to B to C along the rim (Fig. 4.22).

  • Distance travelled = the length of the curved arc ABC actually followed along the circle.
  • Displacement = the straight line AC, joining the starting and finishing positions, directed from A towards C.

The two are not equal: the arc bulges outward while the chord cuts straight across, so arc ABC > chord AC.

Why it happens: on a circular path the object is turning at every instant, so it is never travelling straight towards its destination. Every bit of the arc is longer than the straight-line progress it makes. This gap between path length and net change in position is the clearest reason why we need two separate quantities — distance and displacement — rather than one.
Q2.
What is the distance travelled by the child in making one revolution (going round the circle once)?
Answer

One full revolution means going all the way round the rim once, so the distance travelled is the circumference of the circular path.

distance in one revolution = 2πR
where R is the radius of the circular path

The displacement, on the other hand, is zero, because the child ends the revolution at exactly the same position from which it began.

That is why the two averages part company so dramatically over one revolution. If the revolution takes time T,

average speed, vav = 2πR / T   [Eq. 4.5]
average velocity = displacement / T = 0 / T = 0
Check it yourself: for a merry-go-round of radius R = 2 m turning once in T = 8 s, vav = 2 × 3.14 × 2 m / 8 s = 12.6 m / 8 s = 1.6 m s⁻¹, while the average velocity over that revolution is 0 m s⁻¹.
Q3.
In case of uniform circular motion, the speed is constant but what about the direction of velocity at an instant? Is it changing?
Answer

Yes, the direction changes continuously — at every single instant. The velocity at a point is directed along the tangent to the circle at that point, in the direction of motion, and the tangent turns as the object goes round.

The book's argument with the rectangular and hexagonal tracks (Fig. 4.23) shows why. On a rectangle the runner changes direction 4 times per lap; on a hexagon, 6 times. Increase the number of sides and the turns become more frequent and each one smaller. In the limit, the track becomes a circle — each side shrinks to a point, and the turning never stops.

Why it happens: velocity is not a number, it is a magnitude and a direction. A change in either one is a change in velocity, and a changing velocity means non-zero acceleration. So uniform circular motion is accelerated motion, even though the speedometer reading would never move. We usually say a vehicle is "accelerating" only when its speed changes, and so we miss the acceleration that a car actually has while taking a circular turn at a steady speed.
Check it yourself: Activity 4.5 makes the tangent visible. Lift the ring while the marble is circling inside it, and the marble shoots off in a straight line — along the tangent at the instant it was freed, which is the direction its velocity had at that moment.
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